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Unclarity with Nonstructural Restrictions on Axioms #15

Closed GoogleCodeExporter closed 9 years ago

GoogleCodeExporter commented 9 years ago 
See:
   <http://lists.w3.org/Archives/Public/public-owl-dev/2007JanMar/0218.html>

Original issue reported on code.google.com by bparsia on 29 Mar 2007 at 9:58

GoogleCodeExporter commented 9 years ago 
The definition of simplicity was indeed cyclic. This has been changed in the 
specification.

The notion of regularity is now not mentioned explicitly anymore.

The following complaint has not been handled:
[[
... each axiom in Ax of the form SubObjectPropertyOf(SUB PE) in Ax
fulfils 
at least one of following conditions:
  * SUB is of the form SubObjectPropertyChain(PE PE)
  * SUB is of the form InverseObjectProperty(PE) and 
  * SUB = SPE where SPE &lt; PE
  * SUB = SubObjectPropertyChain(SPE1 ... SPEn) where n &gt;= 2 and 
        SPEi &lt; PE for 1 &lt;= i &lt;= n
  * SUB = SubObjectPropertyChain(PE SPE1 ... SPEn) where n &gt;= 1 and
        SPEi &lt; PE for 1 &lt;= i &lt;= n
  * SUB = SubObjectPropertyChain(SPE1 ... SPEn PE) where n &gt;= 1 and
        SPEi &lt; PE for 1 &lt;= i &lt;= n
]]
Namely, &quot;or&quot; is the appropriate reading: each line depends on the 
structure of SUB; 
that is, each property inclusion axiom can contain SUB of one of the mentioned 
forms, and this SUB must satisfy the mentioned criteria.

The well-foundedness on the role hierarchy is not a problem: the number of 
roles is 
always finite, since the axiom closure is always finite.

Original comment by borismo...@gmail.com on 23 May 2007 at 5:29